In modems for burst transmission of digital data, rapid carrier and clock synchronization are essential. Typically, frequency correction occurs prior to phase recovery since estimators are sensitive to frequency offsets. In this paper, we derive the bit error rate (BER) performance of a M-ary phase shift keying (MPSK) receiver in a closed form when there is no frequency offset estimator. Then we derive a relationship of the required burst length for certain BER with frequency offset estimator. To obtain the BER=10-4, approximately we need the burst length of 101 at Eb/N0=10 dB and 69 at Eb/N0=15 dB.